Question

Find the slope of the tangent line to the graph of 2y³ + y - 2 = x at (1, 1).

Answer 1

Answer:
`(1)/(7)`

Step-by-step explanation:

The slope tangent line can be calculated with the function's derivative:

`2y^3+y-2=x\\\\6y^2(dy)/(dx) +(dy)/(dx) -0=1\\\\(6y^2+1)(dy)/(dx) =1\\\\(dy)/(dx)=(1)/(6y^2+1)`

Now, plug the values of the coordinate in the derivative to find the slope:

`(dy)/(dx)=(1)/(6y^2+1)=(1)/(6(1)^2+1) =(1)/(6+1) =(1)/(7)`